Triangle Similarity Calculator

The general property of similar triangles is that two triangles are similar if and only if their three corresponding angles are congruent. Consequently, the three corresponding sides are equally proportional.

🔎 Two angles are congruent if they are identical to each other.

We don't have to verify all those conditions to get a triangle similarity proof, as there are three triangle similarity theorems that require less information.

Imagine two triangles: ABC and A'B'C', and see what those statements for triangle similarity say:

• SSS (Side-Side-Side) criteria: this similar triangle property says there's similarity if all the corresponding sides are proportional. Mathematically:

  A′B′AB​=B′C′BC​=A′C′AC​A′B′AB​=B′C′BC​=A′C′AC​

• SAS (Side-Angle-Aide) criteria: If two pairs of sides are proportional and the angles between them are congruent, there's similarity:

  If A′B′AB​=B′C′BC​A′B′AB​=B′C′BC​, and ∠ABC∠ABC is congruent to ∠A′B′C′∠A′B′C′, there's similarity.

• AA (Angle-Angle) criteria: the AA triangle similarity criteria says if two pairs of corresponding angles are congruent, that's proof of triangle similarity. For example:

  If ∠BAC∠BAC is congruent to ∠B′A′C′∠B′A′C′ and ∠ABC∠ABC is congruent to ∠A′B′C′∠A′B′C′, thanks to the angle sum property, we know that ∠ACB∠ACB is congruent to ∠A′C′B′∠A′C′B′ and the triangles are similar.

Apart from this geometry triangle similarity tool, you can look at these other calculators:

• Similar triangles calculator;
• Solve similar triangles calculator;
• Triangle scale factor calculator; and
• Triangle proportionality theorem calculator.